Microchannel reactors are one of the most successful implementations of the process intensification concept. Reduced geometric dimensions of the flow channels (typically on the order of millimeters) increase the surface-area-to-volume ratio and minimize transport limitations, resulting in a much faster, reaction rate-limited process. Equipment sizes of intensified processes using microchannel reactors are at least one order of magnitude smaller than conventional devices of equivalent capacity, and consequently result in significant capital savings. Additionally, reduced holdups improve process safety and efficiency and make the process more agile. Microchannel reactors have found many industrial applications, notably in small scale gas-to-liquids processing.
The capital and operating cost savings associated with microchannel reactors come at the price of several control challenges. The combination of unit operations (heat exchange, reaction, fluid flow) in a single device results in a loss of degrees of freedom. Additionally, reduced dimensions make it difficult to incorporate distributed sensors and actuators, thus limiting the control of such reactors to a boundary approach based on sensing and adjusting the channel output and, respectively, input properties.
For steam methane reforming applications, the operation is typically autothermal, i.e., an exothermic reaction provides heat to an endothermic set of reactions that are carried out in parallel, alternating channels. While autothermal designs avoid the need for an external heating medium, they can be more challenging to operate. Heat generation in the exothermic channels must be coordinated with heat consumption in the endothermic channels. Improper alignment (in the axial dimension) of heat fluxes can result in the formation of hotspots (if local heat generation exceeds consumption) or reactor extinction. Several published design concepts for autothermal microchannel reactors seek to improve steady-state temperature and conversion profiles and limit the advent of hotspots in steady-state operation. Among these are distributed feed designs, in which reactants are fed at multiple points along the reactor, offsetting the active sections of the catalyst coatings, which shifts the consumption and release of heat towards the center of the reactor, and segmented combustion catalyst designs which more finely modulate heat generation along the reactor. However, very few studies have focused on the dynamic challenges associated with the operation of microchannel reactors.
Bimetallic strips convert temperature change into mechanical displacements. The bimetallic strips include two metal strips. Each metal strip has a thermal expansion coefficient that is different from the thermal expansion coefficient of the other metal strip. The metal strips are fixedly or rigidly attached at both ends (e.g., by riveting, brazing, or welding). Assuming that the bimetallic strip is flat at the reference temperature (Tref), heating the bimetallic strip results in a deflection of the bimetallic strip in one direction (towards the metal strip having a smaller thermal expansion coefficient α1), while cooling results in the bimetallic strip deflecting in the opposite direction (toward the metal strip having a larger thermal expansion coefficient α2). A deflection of the bimetallic strip due to heating the bimetallic strip is shown in FIG. 1B. Bimetallic strips have found applications in clocks, thermostats, and electrical devices as mechanical temperature sensors. In these applications, displacement of the free end of the bimetallic strips typically moves another structure, such as a valve stem or a switch.
The curvature of the bimetallic strips can be computed as a function of temperature based on the physical properties of the two metals. If one end of the strip is fixed (e.g., to a surface), and the other end of the strip is free to deflect, the deflection, d, of the free end can be related to the temperature of the bimetallic strip by Equation 1 below:
                    d        =                              3            ⁢                                                            L                  strip                  2                                ⁡                                  (                                      1                    +                    m                                    )                                            2                        ⁢                          (                                                α                  2                                -                                  α                  1                                            )                        ⁢                          (                              T                -                                  T                  ref                                            )                                                          H              strip                        ⁡                          [                                                3                  ⁢                                                            (                                              1                        +                        m                                            )                                        2                                                  +                                                      (                                          1                      +                      mn                                        )                                    ⁢                                      (                                                                  m                        2                                            +                                              1                        /                        mn                                                              )                                                              ]                                                          (        1        )            
The deflection, d, is measured from the flat surface to the tip, and Lstrip and Hstrip are the length and thickness of the bimetallic strip at the construction temperature, respectively. The values m and n are ratios of the metal thicknesses (H1/H2) and Young's moduli, respectively. α1 and α2 are the thermal expansion coefficients of the two metals used in the bimetallic strip. T is the temperature of the bimetallic strip, and Tref is the temperature at which the anchor surface and bimetallic strips are constructed (here, assumed to be 25° C.).
In an exemplary reactor model, a catalytic plate microchannel reactor operates autothermally, e.g., an exothermic reaction (combustion of methane) takes place in one set of channels and provides heat for an endothermic reaction (steam methane reforming reactions) occurring in alternating channels. The base case model is shown in FIG. 2 with parameters given in Table 1 below.
TABLE 1Nominal reactor system parametersParameterValueReactor Length63.4cmReforming Channel Height2.0mmCombustion Channel Height2.0mmPlate Thickness0.5mmReforming Catalyst Height20pmCombustion Catalyst Height20pmReforming Inlet Temperature793.15KCombustion Inlet Temperature793.15KReforming Inlet Velocity4.0m/sCombustion Inlet Velocity3.0m/sReforming Inlet Pressure1.085barCombustion Inlet Pressure1.085barReforming Catalyst Offset25.8cm (from left)Combustion Catalyst Offset31.6cm (from right)Reforming Inlet Composition19.11%CH4(Mass Fraction)72.18%H2O2.94%CO20.29%H25.48%N2Combustion Inlet Composition5.26%CH4(Mass Fraction)22.00%O272.65%N2
In one implementation, at least a portion of each channel has an offset catalyst coating, where the coated portions are located so as to coordinate heat generation and consumption and maximize methane conversion.
The reforming reactions occurring in the endothermic channels are as follows:CH4+H2OCO+3H2 ΔH=+206 kJ mol−1  Methane steam reforming (1)CO+H2OCO2+H2 ΔH=−41 kJ mol−1  Water-gas-shift (2)CH4+2H2OCO2+4H2 ΔH=+165 kJ mol−1  Reverse methanation (3)
The reaction kinetics for a 15.2% Ni/Mg/Al2O3 catalyst are described accurately over a wide range of temperatures and pressures by the Langmuir-Hinshelwood-Hougen-Watson approach developed by Xu et al. See J. G. Xu and G. F. Froment, Methane steam reforming, methanation and water-gas shift 0.1. Intrinsic kinetics. AlChE J., 35(1):88-96, 1989.
Catalytic and homogeneous combustion of methane occurs in the alternate channels and in countercurrent flow.CH4+2O2→CO2+2H2OΔH=−803 kJ mol−1  Methane combustion (4)
The reaction kinetics for catalytic combustion on a noble metal catalyst (e.g., Pd or Pt) are first order and zeroth order with respect to methane and oxygen concentration, respectively. Homogeneous combustion has a measurable effect and the kinetics are given by a rate law of order −0.3 with respect to methane and 1.3 with respect to oxygen.
The model reactor considers the combustion and reforming half-channels (with symmetry boundary conditions at the channel centers), the combustion and reforming catalyst layers, and the metal plate. Two-dimensional convection-diffusion-reacting flow is modeled in the channels assuming a laminar, parabolic flow profile between infinite parallel plates. A 1-dimensional model assuming a negligible thickness is used for the catalyst layers, and a 2-dimensional heat equation is used to model the plate.
The model was developed and solved in gPROMS. Backward and forward finite differences were used to discretize the partial derivatives in the axial domains for the reforming and combustion channels, respectively, while central finite differences were used to discretize the partial derivatives in the axial domain of the plate. Orthogonal collocation on finite elements were used to discretize the partial derivatives in the radial domain of every layer. The complete set of model equations are available in previous work and are included at the end of this specification.